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Increasing interest in chemotaxis or cell migration in the presence of concentration gradient of certain chemical species has motivated the need for generating stable uniform concentration gradients in fluid systems. To this end, microfluidic devices have been used for studying chemotaxis over the last two decades. However, challenges in generating stable concentration gradients persist since small fluctuations in pressure or flow rates can destabilize the concentration gradient which may take considerable time to re-establish. In the present work, we propose a novel microfluidic device and optimize several design parameters using computational fluid dynamics simulations to obtain robust uniform chemical gradients. We modified a microfluidic device with a standard Y-shaped ladder design, which originally comprised of one outlet and two inlet streams, by introducing an optimized contact zone for inlet streams and a secondary outlet from this contact zone. Our simulations show that such a device can withstand flow differences as high as 50% between the inlet streams without adversely affecting the concentration gradient generated under ideal conditions (equal flow rate at the inlets).